All Questions
5 questions
3
votes
1
answer
567
views
Projectively flat connection
Let $E \to B$ be a Hermitian vector bundle. If $E$ has a projectively flat connection, then its total Chern character has the form $\mbox{ch}(E) = \mbox{rank} \cdot \exp(\mbox{slope})$. Is the ...
- 363
5
votes
1
answer
411
views
Curvature as infinitesimal holonomy 2
This question may be seen as a follow up of this original question. I'm learning Cheeger-Simons differential characters (reading Differential Characters of Bär and Becker).
If I understand correctly, ...
- 1,347
6
votes
0
answers
156
views
Geometric theory for cohomology groups $H^p(M;\mathbb{Z})$
An excerpt from the book Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski is mentioned below:
Characteristic classes are certain cohomology classes associated
...
- 6,023
2
votes
1
answer
454
views
Advantages of Atiyah sequence version of connections on a principal bundle
I am reading Lie Groupoids and Lie Algebroids in Differential Geometry
by Kirill Mackenzie.
In appendix (page $291$), before discussing about Atiyah sequence associated to a Principal bundle, the ...
- 6,023
4
votes
0
answers
400
views
Chern-Weil theory and Weil homomorphism of principal bundle
In Kobayashi and Nomizu's book Foundations of Differential geometry they introduce the concept of connection on a principal $G$ bundle. In this book, they use connection on a principal bundle to ...
- 6,023